Low intermediate frequency (IF) receiver architectures are attractive due to their improved immunity to DC offsets and flicker noise (i.e., a well known low frequency phenomenon, often called 1/f noise). However, gain and phase mismatches between the in-phase (i.e., I) and quadrature (i.e., Q) paths of a quadrature low-IF receiver (i.e., I/Q mismatch) can result in an image of a nearby interferer falling into a signal of interest. For example, a low-IF Groupe Spéciale Mobile (GSM) receiver requires an image rejection ratio (IRR) of at least 32 decibels (dB) for an IF of 100 kilohertz (kHz) and 50 dB for an IF of 200 kHz. However, typical implementations of such low-IF receivers may only guarantee 25-35 dB of IRR. Thus, low-IF receivers typically require some form of I/Q mismatch compensation.
FIG. 1 is a block diagram illustration of a portion of an example prior-art low-IF quadrature receiver 100 including I/Q mismatch compensation. The quadrature receiver 100 contains an antenna 105 used to receive a wireless radio frequency (RF) signal from a transmitter (e.g., wireless base station) (not shown). To process the RF signal received from the transmitter via the antenna 105, the example quadrature receiver 100 includes a RF receiver 110 that, among other things, demodulates the RF band signal received from the antenna 105 to form quadrature analog low-IF or base-band signals.
To handle conversion from the analog domain to the digital domain, the example of FIG. 1 further includes an analog low-IF/base-band receiver 115. The analog low-IF/base-band receiver 115 includes low-pass filters (not shown), analog-to-digital (A/D) converters (not shown), etc. to transform the quadrature analog IF band signals received from the RF receiver 110 into quadrature digital IF band signals. To further reduce the sampling rate required to represent the quadrature digital IF band signals, the quadrature receiver 100 includes digital filters 120 that include a plurality of digital filters (not shown) and sample rate decimators (not shown). For example, in a low-IF GSM receiver, the input sampling rate of the digital filters 120 could be 430-500 million samples per second (Msps) with an output sampling rate of 1.08333 Msps (i.e., 4 times the GSM baud rate of 270.833 kilo baud per second (Kbs)).
In the example quadrature receiver 100 of FIG. 1, in-phase and quadrature components 122 (i.e., quadrature signals that make up the signal u(n) 122) from the digital filters 120 are provided to an I/Q mismatch compensator 125. The I/Q mismatch compensator 125 adaptively filters the signal u(n) 122 to compensate for I/Q mismatch present in the signal u(n) 122. An output v(n) 127 (comprised of quadrature signals) of the I/Q mismatch compensator 125 is provided to a zero-IF demodulator 130 that digitally demodulates the signal v(n) 127 to a digital baseband signal that is processed by a digital receiver 135. The digital receiver 135 performs, among other things, constellation decoding, error correction, de-framing, etc.
The I/Q mismatch compensator 125 of FIG. 1 computes the output signal v(n) 127 as a difference between the signal u(n) 122 and a filtered version of the signal u(n) 122. In the example of FIG. 1, the filtered version of the signal u(n) is formed as an output of a multiplication of a complex-conjugate of the signal u(n) 122 with a single complex-valued filter coefficient w(n). Thus, complex-valued output v(n) 127 can be expressed mathematically as shown in Equation 1.v(n)=u(n)−w(n)·u(n)*  (Equation 1)
In Equation 1, u(n)=uI(n)+j·uQ(n) represents the complex-valued signal u(n) 122, j is equal to √{square root over (−1)}, w(n)=wI(n)+j·wQ(n) is the complex-valued filter coefficient, * represents the complex conjugate operator, n is an index into a plurality of complex-valued digital samples that make up the complex-valued signals u(n) 122 and v(n) 127, a subscript I represents an in-phase portion of a signal, and a subscript Q represents a quadrature portion of a signal.
The I/Q mismatch compensator 125 of FIG. 1 also includes an adaptive de-correlator 140 that adapts the filter coefficient w(n) to compensate for I/Q mismatch present in the signal u(n) 122 by minimizing gain and phase mismatches between I and Q portions of the signal v(n) 127 (i.e., the gain and phase mismatch between vI(n) and vQ(n)). In particular, adaptation of w(n) can be expressed mathematically as shown in Equations 2 and 3.wI(n+1)=wI(n)+μ·(vI(n)2−vQ(n)2)  (Equation 2)wQ(n+1)=wQ(n)+2·μ·vI(n)·vQ(n)  (Equation 3)
In Equations 2 and 3, μ is an adaptation step-size, a subscript I represents an in-phase portion of a signal, and a subscript Q represents a quadrature portion of a signal. Equation 2 recognizes that I/Q gain mismatch appears as a difference in the signal power between the I and Q portions. In other words, when the power of the in-phase component is equal to the power of the quadrature component, the next value of wI will be identical to the current value of wI. Equation 3 represents the fact that I/Q phase mismatch appears as a non-zero cross-correlation between the I and Q portions. In other words, when the cross-correlation of the in-phase and quadrature components is zero, the next value of wQ will be identical to the current value of wQ.
I/Q mismatch present in a quadrature receiver can vary over time with ambient temperature, frequency of the received signal, and analog gain present in the quadrature receiver, etc. As discussed above, I/Q mismatch manifests itself as an unwanted frequency or signal image and, in the presence of strong interferers adjacent to the desired signal, can result in degraded receiver performance.
The example discussed above in connection with FIG. 1 uses least mean squares (LMS) techniques to adapt the filter coefficient w(n) to compensate for I/Q mismatch present in the signal u(n) 122. It has been recognized that when LMS adaptation is performed simultaneously with actual data reception that the LMS adaptation process may introduce undesired artifacts prior to convergence of the LMS adaptation. Such artifacts may be particularly problematic in situations requiring fast convergence or re-convergence and can lead to instability in the LMS adaptation. Even with a small adaptation step-size (that results in slow re-convergence), a partially adapted filter coefficient may perform I/Q mismatch compensation worse than a previously trained coefficient or a fully re-converged filter coefficient.
In FIG. 1, and in subsequent figures, a signal that includes both the I and the Q portions of the signal is illustrated using a heavy (i.e., bold) line (for example the signal 127 in FIG. 1). When referring to such signals in associated discussions, it is assumed that both portions are included unless explicitly noted. Further, a subscript I represents an in-phase portion of a signal, a subscript Q represents a quadrature portion of a signal, and unless necessary for clarity, time indices for a plurality of digital samples are dropped. For example, the signal 122 is denoted by u, which refers to u(n)=uI(n)+j·uQ(n).